Piotr Pikul

Property Suggestion: Locally orderable

3

## Property Suggestion A space is said to be **Locally orderable** (*Locally ordered topological space*) provided it admits an open cover consisting of LOTS [P133](https://topology.pi-base.org/properties/P000133). According to pi-Base convention this...

Theorem Suggestion: Paracompact + pseudocompact => compact

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## Theorem Suggestion If a space is: - [P30](https://topology.pi-base.org/properties/P000030) - [P22](https://topology.pi-base.org/properties/P000022) then it is [P16](https://topology.pi-base.org/properties/P000016). ## Rationale Negative answer to the search https://topology.pi-base.org/spaces?q=+Paracompact+%2B+Pseudocompact+%2B+%7ECompact ## Proof sketch An unbounded function can...

Theorem Suggestion: no closed point => weakly countably compact

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## Theorem suggestions - **no closed point** ~[P107](https://topology.pi-base.org/properties/P000107) $\Rightarrow$ **weakly countably compact** [P21](https://topology.pi-base.org/properties/P000021) - **partition topology** [P185](https://topology.pi-base.org/properties/P000185) + **has closed point** [P21](https://topology.pi-base.org/properties/P000021) $\Rightarrow$ **has isolated point** [P139](https://topology.pi-base.org/properties/P000139) We can look...